Answer:
[tex]f(x)=16\, (\frac{3}{2} )^{x-1}[/tex]
Step-by-step explanation:
Since we are given the common ratio (3/2), all we need to find to define the geometric sequence, is its multiplicative factor ([tex]a[/tex]) that corresponds to the first term of the sequence - remember that all consecutive terms will be generated by multiplying this first value repeatedly by the common ratio (3/2) as shown below:
[tex]f(1)=a\\f(2)=a\,*\,(\frac{3}{2} )\\f(3)=a\,*\,(\frac{3}{2} )^2\\f(4)=a\,*\,(\frac{3}{2} )^3\\f(5)=a\,*\,(\frac{3}{2} )^4[/tex]
Since we are given the information that [tex]f(5)=81[/tex] we can use this to find the value of the first term:
[tex]f(5)=\,a\,*\,(\frac{3}{2} )^4\\81=\,a\,*(\frac{81}{16} )\\a\,*\,81=\,81\.*\,16\\a\,=\,16[/tex]
Notice as well that the first term doesn't contain the common ratio, the second term contains the common ration (3/2) to the power one, the third one contains the common ratio to the power two, the fourth one contains it to the power three, and so forth. So the exponent at which the common ratio appears is always one unit less than the order (x) of the term in question. This concept helps us finalize the expression for the sequence's formula:
[tex]f(x)=16\,*\,(\frac{3}{2} )^{x-1}[/tex]
Answer:
B
The other answer was too long.
One number has a prime factorization of 23.32, and another number has a prime factorization of 22.3°. Which of the
following expressions would equal the greatest common factor of these two numbers?
25.35
23.33
22.32
2.3
Assuming first number is (2^3)(3^2), second number is (2^2)(3^1).
First number: 2 * 2 * 2 * 3 * 3
Second number: 2 * 2 * 3
Both numbers have at least two factors for 2 and one factor for 3.
Their greatest common factor is (2^2)(3).
1. The food bank has 110.9 pounds, or 1,774.4 ounces, of chick in. To the
nearest whole number, how many servings of chicken does this provide?
Answer:
16 servings
Step-by-step explanation:
To calculate the servings of chicken, we need two pieces of information. We need to know how much money the food bank has and how many ounces of chicken is available. This information is given. Therefore, we can work out the servings of chicken by dividing the ounces of by the amount of money.
[tex]=1774.4/110.9=16[/tex]
So 16 servings of chicken can be provided for 110.9 pounds.
If the circle is dilated by a scale factor of 1/4, what will be the length of the new radius?
1 cm
4 cm
20 cm
64 cm
Answer:
Length of new radius 4 cm.
Step-by-step explanation:
Given radius of circle = 16 cm
Circle is dilated with scale factor 1/4
We need to find the new radius
To calculate New radius we need to multiply radius of the circle with the dilated factor.
Hence new radius = [tex]16 \times \frac{1}{4}= 4\cm[/tex]
Hence Length of new radius is 4 cm.
A receipe calls for 3 potatoes to serve 4 people. If Jack is planning to serve a crowd of 20 people, how many potatoes should he use
The sum of two numbers is 50. One number is 112 less than the other. Find the numbers.
Answer:
81 and -31
Step-by-step explanation:
x + (x - 112) = 50
2x - 112 = 50
2x = 162
x = 81
the other number is x-112 = 81 - 112 = -31
Final answer:
To find the two numbers, set up a system of equations based on the given information. Solve the system of equations to find the values of the two numbers, which are -31 and 81.
Explanation:
To find the two numbers, we can set up a system of equations based on the given information.
Let's assume one number is x, and the other number is y.
According to the problem, the sum of the two numbers is 50, so we can write the equation:
x + y = 50
We are also told that one number is 112 less than the other, so we can write another equation:
x = y - 112
Now we can solve this system of equations to find the values of x and y.
Substituting the value of x from the second equation into the first equation, we have:
(y - 112) + y = 50
Combining like terms, we get: 2y - 112 = 50
Adding 112 to both sides of the equation, we have: 2y = 162
Dividing both sides by 2, we get: y = 81
Substituting this value of y into the second equation, we have: x = 81 - 112
Simplifying, we get: x = -31
Therefore, the two numbers are -31 and 81.
Solve the following equation. Then place the correct number in the box provided. x + 2 = 10
To solve this, subtract 2 from both sides, and you end up with x = 8. :)
(1.2x10^5)+(5.35x10^6)
Answer:
5,470,000
do the multiplication first and then add
When adding numbers in scientific notation, align the exponents and then add the coefficients. The sum of 1.2 x 10^5 and 5.35 x 10^6 is 5.47 x 10^6.
Explanation:To add these two numbers in scientific notation, we need to first align the exponents. In this case, we can rewrite the first number as 0.12 x 10^6 and the second number as 5.35 x 10^6. Now, we can add the numbers together:
0.12 x 10^6 + 5.35 x 10^6 = 5.47 x 10^6. Thus, the sum of 1.2 x 10^5 and 5.35 x 10^6 is 5.47 x 10^6.
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help me out pleaseee
Answer:
Option B is the correct choice.
Step-by-step explanation:
The graph is attached below.
We have to find the [tex]x[/tex] intercept meaning the value of the point on[tex]x-axis[/tex] when [tex]y=0[/tex]
So we will put the value of zero [tex](0)[/tex] instead of [tex]y[/tex] in our given equation.
So here we have solved it algebraically.
[tex]y=\frac{3}{4}x-3[/tex]
Putting [tex]y=0[/tex]
[tex]0=\frac{3}{4}x-3[/tex]
[tex]0=\frac{3x-12}{4}[/tex]
Multiplying [tex]4[/tex] both sides.
[tex]0=3x-12[/tex]
Adding [tex]12[/tex]both sides.
[tex]12=3x[/tex]
Dividing with [tex]3[/tex] both sides.
[tex]x=\frac{12}{3}=4[/tex]
So the x-intercept of the given equation is [tex]4[/tex] which can be written as [tex](4,0)[/tex] in terms of coordinates.
Option B [tex](4,0)[/tex] is the correct choice.
In the diagram below of A ABC, DE is a
midsegment of AABC, DE = 7, AB = 10, and
BC = 13. Find the perimeter of ABC.
Answer:
The perimeter is 37
Step-by-step explanation:
there you go
The perimeter of the triangle is 37 units.
What is perimeter?Perimeter is given by the sum of all the sides of any figure.
Given that, ABC, DE is a midsegment of Δ ABC, DE = 7, AB = 10, and BC = 13.
According to the midpoint theorem states that “The line segment in a triangle joining the midpoint of any two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”
Therefore, AC = 2DE
AC = 14
Therefore, perimeter = sum of all sides,
= 10+13+14
= 37
Hence. the perimeter of the triangle is 37 units.
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find the slope that is parallel to the pair of points.
(4,-2),(16,0)
Essentially, the slope that is parallel to the pair is the the slope of the pair of points.
Using the formula [tex]\frac{y_1-y_2}{x_1-x_2}[/tex], the answer is [tex]\frac{-2}{-12}=\frac{1}{6}[/tex]
The measure of the supplement of an angle is 60 degrees less than four times the measure of the complement of the angle. Find the measure of the angle
If the measure of the supplement of an angle is 60 degrees less than four times the measure of the complement of the angle, the required angle will be 40degrees.
Let the measure of the required angle be x
Supplement of the angle = 180 - x ....................1
Complement of the angle = 90 - x
four times the measure of the complement of the angle = 4(90-x)
60 degrees less than four times the measure of the complement of the angle = 4(90-x) - 60 ................................ 2
Equate 1 and 2 to get the unknown value 'x'
180 - x = 4(90-x) - 60
180 - x = 360-4x-60
180 - x = 300 - 4x
Collect the like terms
-x + 4x = 300 - 180
3x = 120
Divide both sides by 3
3x/3 = 120/3
x = 40
Hence the measure of the required angle is 40 degrees
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The measure of the angle is found to be 40 degrees. This was determined by setting up and solving the equation based on the given relationships between the angle's supplement and complement. Therefore, the angle measures 40 degrees.
To find the measure of the angle, let's denote the angle as x. We know the following:
The supplement of the angle is 180 degrees minus the angle: (180 - x).The complement of the angle is 90 degrees minus the angle: (90 - x).According to the problem, the supplement of the angle is 60 degrees less than four times the complement of the angle. Therefore, we have the equation:
(180 - x) = 4(90 - x) - 60
First, expand and simplify the right-hand side:
180 - x = 360 - 4x - 60
Combining like terms, we get:
180 - x = 300 - 4x
Next, add 4x to both sides to start isolating x:
180 + 3x = 300
Then, subtract 180 from both sides:
3x = 120
Finally, divide both sides by 3:
x = 40
Thus, the measure of the angle is 40 degrees.
Graph the line described by y – 3 = -5/6(x + 3).
Answer:
The graph will show what the line is.
Step-by-step explanation:
y-3 = -5/6(x+3)
Distribute first:
y-3= -5/6x - 15/6
-15/6 is negative because when disributing, -5/6, the negative sign will follow it.
Single out the y:
this means to make the y alone! by doing this, just add 3 to the other side
y-3= -5/6x - 15/6
+3 +3
______________
y= -5/6x + 3/6
Simplify:
y= -5/6 +1/2
-> 3/6 can be simplified to 1/2
Find the Y-intercept on the graph
1/2 on the graph is between 0 and 1
Graph the slope:
from the Y-intercept, go down 5 units, and to the right 6 units.
Then you have your graph!
what's the standard form of the equation y=7/6x + 5
Answer:
-7/6x+y=5
Step-by-step explanation:
y=7/6x+5
y-7/6x=5
-7/6x+y=5
The measure of the vertex angle of an isosceles triangle is one-fourth
that of a base angle.
(I also need the equation)
measure of each base angle =
measure of vertex angle =
Answer:
measure of each base angle = 80 each angle
measure of vertex angle = 20
Step-by-step explanation:
x=base angle
2x+ x/4= 180
Multiply everything by 4 to eliminate the fraction
8x+x = 720
9x=720
x=80
80/4=12
Final answer:
In an isosceles triangle where the vertex angle is one-fourth the measure of a base angle, using the properties of a triangle and the Triangle Angle Sum Theorem, we find each base angle measures 80 degrees and the vertex angle measures 20 degrees.
Explanation:
Given an isosceles triangle, where the vertex angle is one-fourth the measure of a base angle, we can find the measures of the angles using the properties of a triangle. From the Triangle Angle Sum Theorem, we know that the sum of the angles in any triangle is 180 degrees.
Let's denote the measure of the base angle as 'b'. Since the triangle is isosceles, both base angles are equal, so we have 2b for the sum of the base angles. The vertex angle, being one-fourth of a single base angle, is ¼×b = b/4. According to the Triangle Angle Sum Theorem, we can write:
2b + (b/4) = 180
Multiplying through by 4 to clear the fraction gives us:
8b + b = 720
Combining like terms:
9b = 720
Dividing both sides by 9 gives us:
b = 80
Now that we have the measure of the base angle, we can find the measure of the vertex angle:
measure of vertex angle = b/4
Substitute b = 80 into the equation:
measure of vertex angle = 80/4
measure of vertex angle = 20
So, the measure of each base angle is 80 degrees, and the measure of the vertex angle is 20 degrees.
On Carol's morning commute, her car tire was punctured by a nail. Carol was able to drive slowly to the garage. Before the tire could be repaired, the air remaining in the tire had to be let out. More than likely, between which points on the graph was this occurring? A) between points D and E B) between points C and D C) between points B and C D) between points A and B
Answer:
It's C and D
Step-by-step explanation:
The points on the graph in which this was occurring is between points C and D.
What is a Graph?This refers to the representation of data on an x-y plane showing the various cardinal points.
Hence, based on the fact that Carol's car is punctured by a nail and she had to drive slowly and then let off all the air in the tire, these actions most likely occurred between points C and D based on the fact that there is a change in speed.
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What is the value of x?
A.) -9
B.) -10
C.) 10
D.) -12
Answer:
A.) -9
Step-by-step explanation:
it is observed that triangles ABL and KML are similar triangles
hence the following ratios are valid:
LA / LK = LB/LM = AB/KM
we can see that LA/LK = LB/LM = 1/2
hence the above ratio becomes
1/2 = AB/KM (rearranging)
KM = 2AB
We are given that KM = (x + 21) and AB = (x + 15)
hence
KM = 2AB
(x + 21) = 2 (x + 15)
x + 21 = 2x + 30
x - 2x = 30 - 21
-x = 9
x = -9
(+4) + (-13) = solve.
Answer: -9
Step-by-step explanation: When your adding and subtracting positives and negatives, it's a good idea to use a number line to visualize what's going on.
When you're simplifying a problem like (+4) + (-13) we start at zero and +4 moves us 4 units to the right along our number line.
From there, -13 then moves us 13 units back to the left so we end up at -9.
Image provided.
Therefore, (+1) + (-13) = -9
Select all of the following that are ordered pairs of the given function.
f(x) = 3- 2х
(-2, -1)
(-1, 5)
(0,3)
(1, 0)
(2, -1)
Answer:
(-1, 5)
(0, 3)
(2, -1)
Step-by-step explanation:
we have
[tex]f(x)=3-2x[/tex]
Remember that
If a ordered pair is a solution of the given function, then the ordered pair must satisfy the given function
Verify each case
case a) (-2, -1)
substitute the value of x and the value of y in the given function and compare the result
[tex]-1=3-2(-2)[/tex]
[tex]-1=7[/tex] ---> is not true
therefore
Is not a ordered pair of the given function
case b) (-1, 5)
substitute the value of x and the value of y in the given function and compare the result
[tex]5=3-2(-1)[/tex]
[tex]5=5[/tex] ---> is true
therefore
Is a ordered pair of the given function
case c) (0, 3)
substitute the value of x and the value of y in the given function and compare the result
[tex]3=3-2(0)[/tex]
[tex]3=3[/tex] ---> is true
therefore
Is a ordered pair of the given function
case d) (1,0)
substitute the value of x and the value of y in the given function and compare the result
[tex]0=3-2(1)[/tex]
[tex]0=1[/tex] ---> is not true
therefore
Is not a ordered pair of the given function
case e) (2, -1)
substitute the value of x and the value of y in the given function and compare the result
[tex]-1=3-2(2)[/tex]
[tex]-1=-1[/tex] ---> is true
therefore
Is a ordered pair of the given function
The sum of two numbers is 66. The difference of the same two number is 38. What are the numbers?
Answer:
37 and 29
Step-by-step explanation:
x + y = 66
x - y = 8
*******************************************
solve second equation for x
x = y + 8
substitute for x in first equation
y+8 +y = 66
2y = 58
y = 29
*******************************************
x - 29 = 8
x = 37
******************************************
x = 37 and y = 29
Final answer:
To solve for the two numbers, set up equations based on the sum and difference provided. By solving these equations, we find that the numbers are 52 and 14.
Explanation:
The sum of two numbers is 66, and their difference is 38. This problem can be solved using a system of equations. Let's denote the two numbers as x and y.
According to the information given:
x + y = 66 (Equation 1)x - y = 38 (Equation 2)Now, we can solve these equations simultaneously.
Add Equation 1 and Equation 2: (x + y) + (x - y) = 66 + 38, which simplifies to 2x = 104. Therefore, x = 52.Substitute x = 52 into Equation 1: 52 + y = 66, so y = 66 - 52, which gives us y = 14.The two numbers that satisfy the conditions of the problem are 52 and 14.
The circle with center F is divided into sectors. In circle F , EB is a diameter. The radius of circle F is 3 units
Answer:
This is only if you are looking to find the Arch AED 11pi/4
Step-by-step explanation:
See photo
Arc length AED of a given circle with a radius of 3 units is 11π/4.
According to the given diagram,
The angle subtended by arc AED or central angle = 360°-120°-45°-30° = 165°
The radius of the circle = 3 units
What is the relationship between arc length, central angle and radius?Arc length = Central angle(in radians) * Radius
So, arc length AED = 165 *π/180 * 3
Arc length AED = 11π/12 * 3 = 11π/4
Therefore, the Arc length AED of a given circle with a radius of 3 units is 11π/4.
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7. What is the value of x in the equation 2x + 4 =-42?
A. -19
... -7
B. -23
D. Not Here
Answer:
B. -23Step-by-step explanation:
2x + 4 = -42 subtract 4 from both sides
2x + 4 - 4 = -42 - 4
2x = -46 divide both sides by 2
2x/2 = -46/2
x = -23
Steps To Solve:
2x + 4 = -42.
2x + 4 - 4 = -42 - 4
2x = -46
2x/2 = -46/2
x = -23 (Answer)
______
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. it will cost 6500 to rent trucks plus 225 for each ton of sugar transported. the total cost, C (in dollars), for transporting n tons is given by the following function
Answer:
C = 6500 + 225n
Step-by-step explanation:
It will cost $6500 to rent a truck plus $225 for each ton of sugar transported.
So, in the equation which relates the total cost for transporting sugar in a truck, $6500 will be the initial value and $225 will be the rate of transporting sugar per ton.
Hence, for transporting n tons of sugar, the total cost C in dollars is given by the following equation
C = 6500 + 225n (Answer)
Cos^2(2theta)+ 2cos(2theta)+1=0
Answer:
θ = π n + π/2 for n element Z
Step-by-step explanation:
Solve for θ:
1 + 2 cos(2 θ) + cos^2(2 θ) = 0
Write the left hand side as a square:
(cos(2 θ) + 1)^2 = 0
Take the square root of both sides:
cos(2 θ) + 1 = 0
Subtract 1 from both sides:
cos(2 θ) = -1
Take the inverse cosine of both sides:
2 θ = 2 π n + π for n element Z
Divide both sides by 2:
Answer: θ = π n + π/2 for n element Z
Questions:
Which display is more useful for approximating the minimum distance?
Which display can be used to find that there were 23 vehicles at Nam’s Used Car Lot?
Answer:
See explanation
Step-by-step explanation:
Which display is more useful for approximating the minimum distance?
More useful is box-and-whisker plot (second display) because there you can exactly see that the minimum distance is 10 km (left point at the plot).
Which display can be used to find that there were 23 vehicles at Nam’s Used Car Lot?
More useful is first display, because you see the following information:
Distance Number of vehicles
0 - 50 3
50 - 100 4
100 - 150 5
150 - 200 6
200 - 250 3
250 - 300 2
Total number of vehicles = 3 + 4 + 5 + 6 + 3 + 2 = 23
Answer:
23 vehicles
I'm on khan academy right now and its 23
( please help me )THIS SEEMS SIMPLE BUT CAN SOMEONE HELP!!!!!!!!! I WILL MARK BRAINLEST
1. Positive but not perfect: Figure 4
2. Correlation coefficient equal to 1:
3. Strongest linear relationship: Figure 2
Step-by-step explanation:
"Correlation is the link between two quantities"
The relationship is said to be positive if both are increasing and said to be negative if both are opposite i.e. one is increasing and one is decreasing.
In the Given figures
1. Positive but not perfect linear relationship:
The perfect positive relationship is when both the quantities are increasing and the scatter points are in a line that grows linearly. Here, The data set in figure 4 has positive correlation but as the points are scattered around a line so the correlation is positive but not perfect.
2. Correlation equal to 1
The correlation in figure 1 is the perfect correlation as the data points follow a straight line and both the quantities are increasing.
3. Strongest linear relationship:
The relationship in figure 2 has the strongest in figure 2 as the data points are more close to the best fit line
Keywords: Correlation, Scatter Plot
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Which of the following is equivalent to -17/9
Which set of values could be from a direct proportion?
Answer:
The second option
Step-by-step explanation:
The second option because it is the one in which if you multiply f4 to the values of x, you would get y.
And that is why it is the second option.
Please help me solve 3x+x=2x+2. Can you please break down step by step
Answer:x=1
Step-by-step explanation:
fist add like- terms in either side of the equation:
4x=2x+2.
next, you want to get both the X's on the same side of the equation. this means you need to subtract 2x from the left side of the equation and bring it to the right side of the equation. this means you have to subtract 2x from 4x. because what you do on one side of the equation you have to do on the other.
2x=2
next divide each side of the equation to get x alone.
x=1.
9. The approximate circumferences of Earth
and Saturn are shown. How many times
greater is the circumference of Saturn than
the circumference of Earth?
C = 365,882 km
The circumference of Saturn is
x 10 km.
C = 4,01 x 104 km
Saturn's circumference is about times
greater than the circumference of Earth.
(4 x 105)-(4.01x104)
400,000
4x 103 km
10. Estimate 0.037854921 to the nearest hundredth.
11. Compare the numbers 6 x 10-6 and 2 x 10-8.
Answer:The greater value is 600 x 10⁻⁸. And the lesser value is 2 x 10⁻⁸. The number 600 x 10⁻⁸ is 300 times greater number 2 x 10⁻⁸.
Step-by-step explanation:⇒ 6 x 10⁻⁶ and 2 x 10⁻⁸⇒ 600 x 10⁻⁸ and 2 x 10⁻⁸The number 600 x 10⁻⁸ times greater than the number 2 x 10⁻⁸ will be ⇒ 600 x 10⁻⁸ / 2 x 10⁻⁸⇒ 300
Final answer:
The circumference of Saturn is not greater than that of Earth; Earth's circumference is greater. Saturn's circumference at 40,100 km is approximately 0.11 times that of Earth. Also, 0.037854921 rounded to the nearest hundredth is 0.04, and 6 x 10⁻⁶ is larger than 2 x 10⁻⁸.
Explanation:
To answer how many times greater the circumference of Saturn is than the circumference of Earth, we need to compare the two given circumferences. The circumference of Earth is 365,882 km, and the circumference of Saturn is given as 4.01 x 10⁴ km.
First, we convert Saturn's circumference to a standard numerical form: 4.01 x 10⁴ is 40,100 km. Now, we can divide the circumference of Saturn by the circumference of Earth: 40,100 km / 365,882 km which roughly equals 0.11. This means that Saturn's circumference is about 0.11 times the circumference of Earth, which indicates that Earth's circumference is actually greater, not Saturn's.
For the second part, estimating 0.037854921 to the nearest hundredth would result in 0.04 because the third digit after the decimal is 7, which rounds the second digit up to 4.
Comparing the numbers 6 x 10⁻⁶ and 2 x 10⁻⁸, 6 x 10⁻⁶ is larger because it is only 10⁻⁶ compared to 2 x 10⁻⁸ which is much smaller being 10⁻⁸.
A 55% decrease followed by a 25% increase A 75% increase followed by a 3313% decrease A 20% decrease followed by a 40% increase A $30 increase followed by a $30 decrease A 100% increase followed by a 50% decrease
Answer:
Part 1: Less.
Part 2: Greater.
Part 3: Greater.
Part 4: Less.
Part 5: Equal.
Step-by-step explanation:
Part 1: Assume that the value is x initially.
So, 55% decrease of value of x will give [tex]x(1 - \frac{55}{100}) = 0.45x[/tex].
Again, 25% increase of the value obtained will give [tex]0.45x(1 + \frac{25}{100}) = 0.45 \times 1.25 \times x = 0.5625x[/tex]
So, it is less than x. (Answer)
Part 2: Assume that the value is x initially.
So, 75% increase followed by [tex]33\dfrac{1}{3} = 33.33[/tex]% decrease will give [tex]x \times (1 + 0.75) \times (1 - 0.333) = x \times 1.75 \times 0.667 = 1.167x[/tex]
So, it is greater than x.
Part 3: Assume that the value is x initially.
So, 20% decrease followed by 40% increase will give [tex]x \times (1 - 0.2) \times (1 + 0.4) = x \times 0.8 \times 1.4 = 1.12x[/tex]
So, it is greater than x.
Part 4: Assume that the value is x initially.
So, 30% increase followed by 30% decrease will give [tex]x \times (1 + 0.3) \times (1 - 0.3) = x \times 1.3 \times 0.7 = 0.91x[/tex]
Hence, it is less than x.
Part 5: Assume that the value is x initially.
So, 100% increase followed by 50% decrease will give [tex]x\times (1 + 1) \times (1 - 0.5) =x \times 2 \times 0.5 = x[/tex]
Hence, the final value is same as x. (Answer)
Answer:
the pictures uppppppppp